The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.
A Mathematical Tour
A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.
Amusements in Mathematics
Unlock the Enigma of Numbers with a Timeless Classic! Dive into the captivating world of ""Amusements in Mathematics"" by the legendary Henry Ernest Dudeney, a masterpiece that has enchanted puzzle enthusiasts for generations. This extraordinary collection of mathematical puzzles and brainteasers, once out of print for decades, is now beautifully republished by Alpha Editions, making it a must-have collector's edition for both the curious minds of today and the inquisitive thinkers of tomorrow. From mind-bending riddles to ingenious conundrums, Dudeney's brilliance shines through every page, offering a delightful challenge to both novice and seasoned puzzle solvers. Whether you're looking to sharpen your problem-solving skills or simply seeking an entertaining escape into the world of numbers, this book promises hours of intellectual amusement. Don't miss your chance to own a piece of mathematical history that has stood the test of time. Rediscover the joy of puzzles with ""Amusements in Mathematics"" and let your imagination soar!
Engaging Young Student Math (V3)
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Course in Ordinary Differential Equations with Applications
This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices.
Jewish Calendar Mathematics
This book begins with a short overview of calendars in general, and then delves deeply into Jewish calendar structure and mathematics. Details of how Torah portions are scheduled and how the structured triennial Torah reading and haftorah reading cycles work are explained. A comprehensive explanation of the calendrical aspects of Jewish holidays as well as the relationships between them and non-Jewish holidays is included. There are fourten appendices which allow even greater visibility into the material than does the main narrative by itself. This volume also includes substantial new material absent from the book's predecessor. A glossary is provided.
Various Studies on Split and Non- Split Dominating Sets of an Interval
Square-Free Factorizations. Some Cryptological and Other Mathematical Aspects
Set Dynamic Equations on Time Scales
The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.
Graph-Theoretic Concepts in Computer Science
This book constitutes the refereed proceedings of the 50th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2024, held in Gozd Martuljek, Slovenia in June 2024, The 31 papers presented in this volume were carefully reviewed and selected from 89 submissions. Additionally, this volume also contains a survey on approximation algorithms for tree-width, path-width, and tree-depth prepared by Hans Bodlander, who delivered the Test of Time Award talk at WG 2024. The WG 2024 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science or by extracting new graph-theoretic problems from applications.
Geometry by Its Transformations
This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid's Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the M繹bius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.
Almost Periodicity and Almost Automorphy
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an "ordinary differential equation" with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Discrete Mathematics
This book aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors. This course serves both as a survey of the topics in discrete math and as the "bridge" course for math majors.
Introduction to Enumerative and Analytic Combinatorics
These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.
Advances in Fuzzy Logic and Artificial Neural Networks
In a world where uncertainty and complexity dominate decision-making processes, Advances in Neural Networks and Fuzzy Logic presents groundbreaking studies exploring the potential of these Artificial Intelligence approaches to solve real-world problems. The chapters cover applications across various fields, such as robust galaxy classification, simulations in weighted finite automata, stock price prediction, large-scale water purification selection, speech deficiency detection in children, and supply chain management. Advanced techniques such as deep neural networks, fuzzy clustering, SHAP, LIME, and Hesitant Fuzzy Linguistic Term Sets are explored. This reprint is helpful for researchers, engineers, and students who wish to understand the latest advancements in and practical applications of neural networks and fuzzy logic. Within these pages, you will discover how these technologies solve complex problems and foster more transparent and reliable decision-support systems, as well as the state of the art in Artificial Intelligence, where neural networks and fuzzy logic converge to tackle modern challenges with innovation and precision.
The calculating engine
The calculating engine" is a classic book, that has held significant value throughout history, and to ensure its timeless wisdom is never lost, Alpha Editions has carefully preserved it by republishing it in a modern, accessible format for both present and future generations. Thoughtfully reformatted, retyped, and newly designed, this edition offers a clear and readable text-free from scanned copies of the original work. Alpha Editions is dedicated to breathing new life into antique and classic books, making these literary treasures available once again for readers who cherish history, culture, and timeless knowledge.
